Details

Time bar (total: 8.2s)

sample14.0ms

Algorithm
intervals
Results
4.0ms256×body80valid
1.0ms82×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
7.0ms
(sqrt (+ x 1.0))
32.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series211.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
31.0ms
(sqrt (+ x 1.0))
139.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.5s

Counts
80 → 80
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0146959
1333886
2955819
33894808
done5000807

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
100×*-un-lft-identity
67×add-sqr-sqrt
64×add-cube-cbrt
19×associate-/r*
18×distribute-lft-out
17×add-exp-log
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×pow1 div-inv add-log-exp
4×cbrt-undiv expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def flip3-+ flip-+
2×rec-exp frac-2neg sqrt-div 1-exp clear-num associate-/l/
1×+-commutative rem-sqrt-square pow-flip sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def inv-pow
Counts
4 → 161
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
48.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
35.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series290.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(sqrt (+ x 1.0))
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
83.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
134.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify821.0ms

Counts
173 → 173
Iterations

Useful iterations: done (816.0ms)

IterNodesCost
02592731
16012381
215002133
done50012100

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (+ x 1.0)) 3)
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.3b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u sum-cubes log1p-expm1-u sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 194
Calls
4 calls:
9.0ms
(pow (sqrt (+ x 1.0)) 3)
38.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
27.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
85.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (sqrt (+ x 1.0)) 3)
18.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
65.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
185.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.4s

Counts
206 → 206
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03264145
18042987
229402729
done50002724

prune430.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
288×*-un-lft-identity
190×sqrt-prod
189×add-sqr-sqrt
186×add-cube-cbrt
51×distribute-lft-out
34×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/l*
9×div-inv
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def flip3-+ flip-+
2×frac-2neg sqrt-div clear-num associate-/l/
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def
Counts
4 → 305
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
15.0ms
(+ 1.0 (sqrt (+ x 1.0)))
41.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
52.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

series361.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
140.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
143.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

simplify1.2s

Counts
317 → 317
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03846996
18796291
228655814
done50015716

prune427.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11210
done1210

end0.0ms

sample344.0ms

Algorithm
intervals
Results
153.0ms8000×body80valid
38.0ms2686×body80nan